The Republican establishment woke up Wednesday morning to the reality it has dreaded, that the party might soon have to practice thinking positive thoughts about Donald Trump. The losers on Tuesday could start by cooling the doomsday rhetoric, understanding that they might have to eat some of the harsh words they have been saying about him. He scored far above what was thought to be the limit of his appeal, not only moving past the 50 percent mark, but scoring 60 percent, well above the usual measures of “landslide.” He won 85 of New York’s 95 delegates to the Republican National Convention in Cleveland in July.

The fat lady has not yet sung, to be sure, but she’s moving from the shadows in the wings to wait for her cue close to the stage. Gov. John Kasich of Ohio, the favorite of the elites, finished far behind, and Sen. Ted Cruz of Texas finished a dismal third, where he was barely visible and left to ponder New York values. Whether the Donald can win the 1,237 delegates he’ll need to win the nomination on the first ballot is not yet clear — it’s certainly no sure thing — but the Republican powers-that-be are on notice that it’s probably too late to use tricks and lawyerly magic to deprive Mr. Trump of what he has almost won.

He is only now doing what he should have done months ago, putting together an actual campaign organization. He seems to be abandoning the devil-may-care rhetoric that brought his rallies to full-throated ecstasy, but put off many others. The ecstatic followers will no doubt forgive him if he turns down the heat and softens the volume to reassure skeptics. Someone on the verge of nomination must do that. He must say nice things about rivals he described as “stupid” and “jerks” only yesterday. It’s how the great game of politics actually works.

Many Republican regulars, who understand they have only a limited time to nurse their anger and disappointment, are trying to warm to the Donald. It’s difficult, but the prospect of Hillary Clinton and her coterie of radical hangers-on, waiting to organize Barack Obama’s third term, frightens the wise and the thoughtful to come to full attention for the task at hand. Hillary, too, has flaws. She makes many Democrats, including women, nervous.

Every thoughtful voter is concerned about Mr. Trump’s rude bombast and, more important, his inexperience in the world beyond the jackhammer, the bricks and the mortar of the towers that decorate the Manhattan skyline. But he did not come to town on the turnip truck, and is obviously capable of playing a new game. He has an undeniable instinct for knowing what voters are angry about, and anger wins elections. Exit polls reveal that he won 57 percent of the women’s vote in the New York Republican primary. That’s not caviar, but it’s not peanut butter. Many of the women who don’t like the Donald don’t like Hillary, either.

The disappointed losers of Tuesday are not all Republicans. One new poll finds 20 percent of the friends of Bernie Sanders say they wouldn’t “under any circumstances” vote for Hillary Clinton. But anger cools, disappointment subsides, and after the conventions the usual voting patterns will assert themselves. They always do. America is approximately evenly divided, and is likely to remain that way for the foreseeable future.

This assures a spirited race ahead, with gaffes, mistakes, unforced errors, surprises and pitfalls to make the months ahead interesting for everyone. The doomsday talk of April will give way to less-combustible conversation by the time the first leaves of autumn fly. Bloviation is fun, but it’s important for the captains of the party to remember to keep calm and carry on. The future — the nation’s and their own — depends on it.